# Value-weighted return: which date should the market-capitalization be based on?

I got a short question regarding calculating the value-weighted return of portfolios.

Example:

The portfolio is constructed based on the value of a certain criteria on date 31.1 (Jan 31st). The return for the constructed portfolio is calculated as: the closing price on 28.2 divided by the closing price on 31.1 (as it is also the opening price on 1.2). Which market-capitalization do I chose to weight the individual returns of the companies? Market-capitalization on the day of portfolio construction or the last day of the month in which I calculate the monthly return?

Thanks!

• don't you mean the portfolio return at time $t=T$ is $\frac{P_T}{P_0}-1$ where $t=0$ is the date of portfolio construction and $T$ is the performance measurement date (one month after construction)? – develarist Nov 25 '19 at 18:00
• yes, exactly. Do I use the mcaps on t=1 or t=0? – user43224 Nov 25 '19 at 18:21
• While your argument makes obviously sense, I'm not 100% convinced. For example the S&P500 is value-weighted too. As there is no initial investment (expect maybe the day of the IPO but it doesn't make sense) this is not applicable to them, therefore they probably use something else (probably the market cap for that day/month/period). – user43224 Nov 25 '19 at 19:09